8-7 Solving Systems of Linear Equations – We learned to find the number of solutions to a system of linear equations by graphing. We plotted both lines on the same coordinate plane and identified their intersection behavior. If the lines intersect at one point that was the solution. If the lines were parallel there was no solution and if the lines overlapped there were infinitely many solutions.
Assignment: Complete assigned problems for homework.

Rationalizing the Denominator: Definition, method and example problems. Graphs and Equations of Circles: During today's session on Rationalizing the Denominator, Aiden followed very well this complicated and challenging method. Additional practice in his Critical Thinking Skills class will reinforce his confidence with these types of problems.

Equations and Graphs of Circles: Location of center coordinates, Converting equations into
center coordinates form using Completing the Square method. During today's lesson on Graphing Circles using a standard equation equation form, Aiden was very attentive and was required to use the previously learned Completing the Square method.

Equations and Graphs of Circles: Identifying Center of Circle coordinates, calculating radius from the given equation. Review of Interior and exterior angles of Regular Polygons. Various example/demonstration problems. Review of determining Arc Length of Circles.
During today's lesson of Equations and Graphs of Circles, Aiden was attentive but initially struggled with his focus/concentration. The long-standing issue regarding Aiden's interest in "why" the equations/graphs exist vs "how" equations are used/interpreted to obtain useful results is resurfacing. I am working with him to adjust his focus and interest on key problem-solving skills that matter.

Equations of Circles: Location of Center at (h,k). Various demonstration examples of writing equations for circles with radius R and known coordinates location of the center. During today's new lesson topic on the Equations for Circles, Aiden initially struggled to comprehend the basic characteristics and then clarified his understanding with additional practice examples that were provided.

We learned that an exponential growth function increases by a fixed percent and an exponential decay function decreases by a fixed percent over each interval. We learned to construct exponential growth and decay functions given a description of a relationship. Then we recognized if a situation can be modeled with exponential growth or decay, and interpreted the parameters of the model in context. Next we became familiar with the terms compound interest, exponential growth, and growth factor.

Determining Compound Areas using Algebra. Trapezoids, semi-circles, negative/missing areas etc. Review of Unit Test results. During today's session on determining compound areas using Algebra, Aiden demonstrated very good skill and comprehension.

Key Features of a Quadratic Function – We learned to identify key features of the quadratic function using graphs, tables, and equations. Then we learned the effect of the value of a on the quadratic parent function. We learned that a quadratic function is a polynomial function in one or more variables in which the highest degree term is of the 2nd degree. The graph is a parabola. The value of the leading coefficient determines both the width of the parabola and the direction the parabola opens (upward or downward). We reviewed the attributes of a quadratic function such as minimum/maximum value and symmetry. Then we learned how the attributes affect the shape of a parabola.

Unit Test Geometry and use of Algebra: Full Period. During today's Unit Test on Geometry using Algebra, Aiden worked productively for the entire class period.

Review for Geometry and Algebra Exam